Yang-Mills gauge theories from fermionic lattice models

TL;DR

This paper demonstrates how fermionic lattice models can be used to simulate non-Abelian Yang-Mills gauge theories, including the generation of gauge fields and monopoles, with potential applications in quantum simulations.

Contribution

It introduces a method to encode SU(2) gauge fields in fermionic lattice models and shows how to generate Yang-Mills fields and monopoles in this framework.

Findings

Fermionic lattice models can effectively simulate non-Abelian gauge fields.

Distortion of tunnelling couplings induces scalar and Yang-Mills fields.

Simulation of Yang-Mills monopoles with localized zero-modes.

Abstract

A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We explicitly demonstrate that suitable distortion of the tunnelling couplings can introduce a scalar and a Yang-Mills field in the effective low energy description, both coupled to the Dirac fermions. As an application we simulate Yang-Mills monopoles that give rise to localized zero-modes and fermion fractionalization. The generation of the non-Abelian field in the two-dimensional case is also presented.